CheckUser policy/Local policies

Wikipedia

CheckUsers are elected by the community; they are admins, but do not have any other "higher" local rights (segregation of duties)
local policy is at Wikipedia:Checkuser
CheckUsers only act on request
usually all requests should be made publicly at Wikipedia:Checkuser/Anfragen, fact-based comments by other users are possible
private requests are allowed as an exception (when private data, e.g. real names are affected)
public log exists, requests and decisions are stored on archive pages (see also bdk's indiv. log)
strictly all checks are publicly announced (anonymised if needed, e.g. regarding user names)
CheckUsers do not perform any following blocks/bans themselves

Local policy is described at w:fr:Wikipédia:Vérificateur d'adresses IP
CUs are nominated by the local ArbCom. They are not necessarily admins.
Local requests are at w:fr:Wikipédia:Vérificateur d'adresses IP/Requêtes
CheckUsers do not block accounts themselves, except for open proxies or misconfigured servers

Local policy: here and here (the latter with some English translation, both to be revised in the near future)
Local CU requests: hu:Wikipédia:IP-ellenőrzési kérések#Kérések
Local public log: hu:Wikipédia:IP-ellenőrzési kérések/Napló
Draft of the forthcoming new policy: hu:User:Bináris/elvterv (only for Hungarian speakers)

based on 5 editors' public vote (but there must be more supporting than protesting votes), with valid reason and evidence/suspicion supplied
based on 2 admins' private or public vote
based on 2 editors' common request to prove that they are not each other's sockpuppet

CheckUsers are not allowed to run a check without one of these conditions.

There is a public log, in which all the checks are to be listed, with the minimal content of the date and CU's name.

There is no local policy. According to this decision of Arbitration Committee the Wikimedia wide policy is assumed.
Local CU requests: ru:Википедия:Проверка участников
No public log.

Checks are performed at the CheckUser's discretion.

No local policy, Wikimedia Checkuser policy is assumed.
Requests may come to q:WQ:AN.
No public log. Some reports may come to q:WQ:AN.
Checks are performed at the checkuser's discretion, and reported to the other local checkusers by email.
When a request comes to q:WQ:AN, it is usual to give as detailed a reply as is consistent with privacy, but there is no rule.

See Local policy
Requests may be placed on above-listed page
Checking is at Checkuser's discretion
Checkusers are expected to request an independent CU complete the check where a conflict may exist
Detailed replies will not be given. Only sufficient general information for a course of action to be decided

No local policy; the Meta policy is used.
Checks are performed at the CheckUsers' discretion, though requests could be made at b:WB:AA.
CheckUsers typically perform checks and act on the results independently - there is no request process & detailed results are not revealed. There is no public log.

See local policy.
Checks must either be public, or discussed on checkuser-l.
A meaningful justification for each check must be published on the Wikisource:Administrator's noticeboard whenever one is possible without violating privacy.
Requests at s:en:WS:AN, s:en:User_talk:Jayvdb or s:en:User_talk:Pathoschild.